Scattered Photons

approximation to Klien Nis

k[E_] := 0.52  +  0.07 E/80;

E is photon energy in keV

Plot[
       k[E], {E, 0, 200}, {PlotRange -> {0, 1},
         PlotStyle -> Thickness[0.01]}]

define compton attenuation coef.

f[E_] :=
         0.597 * (10^-24)*           Exp[-0.0028 (E - 30)];

NA  =  6.02 * 10^23;

μcompton[E_, ρ_, Z_,            A_] :=  ρ NA (Z/A) f[E];

ratio of scattered to transmitted

ratio[ρ_, Z_,  A_, L_, E_,
           r_] := μcompton[E, ρ, Z,  A]^2 L 2 k[
             E] (L  +  r  - Sqrt[L^2 + r^2]);

water

Zwater  =  7.54;
Awater  =  16;
ρwater  =  1;

rwater[L_, E_, r_] :=
         ratio[ρwater, Zwater, Awater, L, E, r];

Plot3D[
       rwater[L, E, 10], {L, 1, 20}, {E, 10, 100},  {PlotRange -> All,
         PlotPoints -> {64, 64}}]

bone

Zbone  =  14.2;
Abone  =  21.4;
ρbone  =  2.93;

rbone[L_, E_, r_] :=
         ratio[ρbone, Zbone, Abone, L, E, r];

Plot3D[
       rbone[L, E, 10], {L, 1, 20}, {E, 10, 100},  {PlotRange -> All,
         PlotPoints -> {64, 64}}]

Plot3D[
       rbone[L, E, 10], {L, 0.1, 2}, {E, 10, 100},  {PlotRange -> All,
         PlotPoints -> {64, 64}}]